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The support vector machine (SVM) and minimum Euclidean norm least squares regression are two fundamentally different approaches to fitting linear models, but they have recently been connected in models for very high-dimensional data through…
In this paper we measured the stability of stochastic gradient method (SGM) for learning an approximated Fourier primal support vector machine. The stability of an algorithm is considered by measuring the generalization error in terms of…
This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\to\delta$) drawn from a…
Support vector machines (SVMs) rely on the inherent geometry of a data set to classify training data. Because of this, we believe SVMs are an excellent candidate to guide the development of an analytic feature selection algorithm, as…
Data mining algorithms are originally designed by assuming the data is available at one centralized site.These algorithms also assume that the whole data is fit into main memory while running the algorithm. But in today's scenario the data…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
This paper addresses feature subset selection for Support Vector Machines (SVMs) based on the cross-validation criterion. Unlike statistical criteria such as the Akaike information criterion (AIC) and the Bayesian information criterion…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order…
Objective: Classifier transfers usually come with dataset shifts. To overcome them, online strategies have to be applied. For practical applications, limitations in the computational resources for the adaptation of batch learning…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
Support vector machines (SVMs) are invaluable tools for many practical applications in artificial intelligence, e.g., classification and event recognition. However, popular SVM solvers are not sufficiently efficient for applications with a…
We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector and relies on a quantum linear programming solver instead…
Conventional SVM-based image coding methods are founded on independently restricting the distortion in every image coefficient at some particular image representation. Geometrically, this implies allowing arbitrary signal distortions in an…
The Support Vector Machine (SVM) is one of the most widely used classification methods. In this paper, we consider the soft-margin SVM used on data points with independent features, where the sample size $n$ and the feature dimension $p$…
The support vector machine (SVM) is a well-established classification method whose name refers to the particular training examples, called support vectors, that determine the maximum margin separating hyperplane. The SVM classifier is known…
Support vector machine algorithms are considered essential for the implementation of automation in a radio access network. Specifically, they are critical in the prediction of the quality of user experience for video streaming based on…
Variance reduction (VR) methods employ stochastic gradients with decreasing variance, and they have been widely applied to solve large-scale optimization problems in machine learning because of their efficiency. Existing theoretical studies…
Support Vector Machine (SVM) has been one of the most successful machine learning techniques for binary classification problems. The key idea is to maximize the margin from the data to the hyperplane subject to correct classification on…
This paper investigates the nonparametric regression problem using SVMs with anisotropic Gaussian RBF kernels. Under the assumption that the target functions are resided in certain anisotropic Besov spaces, we establish the almost optimal…